Abstract
In this paper, we investigate the direct and indirect stability of locally coupled wave equations with local viscous damping on cylindrical and non-regular domains without any geometric control condition. If only one equation is damped, we prove that the energy of our system decays polynomially with the rate \(t^{-\frac{1}{2}}\) if the two waves have the same speed of propagation, and with rate \(t^{-\frac{1}{3}}\) if the two waves do not propagate at the same speed. Otherwise, in case of two damped equations, we prove a polynomial energy decay rate of order \(t^{-1}\).
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Akil, M., Badawi, H., Nicaise, S. et al. Stabilization of Coupled Wave Equations with Viscous Damping on Cylindrical and Non-regular Domains: Cases Without the Geometric Control Condition. Mediterr. J. Math. 19, 271 (2022). https://doi.org/10.1007/s00009-022-02164-6
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DOI: https://doi.org/10.1007/s00009-022-02164-6